In a debate with a flat earth friend and need help to make sure I understand this correctly. He points out that the part of earth that is on the outside of its orbit is traveling faster than the inside, so why don't we experience centripetal force as our speed changes. If you spin a basketball on your finger and walk forward, the part of the b-ball moving forward (away from you) is moving faster than the part moving backward (toward you). We feel even slight changes in speed in a car, and this would be a change in hundreds if not thousands of kph. So why don't we feel it? I have a lot of answers floating around in my head, but I'm not absolutely sure I know the correct answer. Can anyone help me out?
If orbital period is constant, centripetal force is proportional to the radius of the orbit. The average radius of the Earth's orbit around the Sun is about $150$ million km. The diameter of the Earth is about $12,700$ km. So the difference in centripetal force from one side of the Earth to the other is about one part in $12,000$.
This difference is certainly too small for us to "feel". However, we do see its effects in tides. The tidal force of the Sun on the Earth is about half that of the Moon. This is why the tidal range is greater when the Moon is new or full (when the Moon and the Sun align) than when the Moon is in its first or third quarter.